It is eternally surprising to me that people keep doing studies of whether democracy affects growth using the same cross-country data but their regular findings—that institutions and the rule of law matter but democracy doesn't—are less of a surprise.
The latest, "Democracy and Growth: A Dynamic Panel Data Study" (pdf) is from Jeffry Jacob, of Bethel University and Thomas Osang of Southern Methodist University:

In this paper we investigate the idea whether democracy can have a direct effect on economic growth. We use a system GMM framework that allows us to model the dynamic aspects of the growth process and control for the endogenous nature of many explanatory variables. In contrast to the growth effects of institutions, regime stability, openness and macro-economic policy variables, we find that measures of democracy matter little, if at all, for the economic growth process.

They look at a full 160 countries over 50 years, building on a large existing literature, which includes (my own picks, not theirs):

Acemoglu et al. (2008) found that once you control for 'country fixed effects' (i.e. systematic and apparently intractable differences between countries) there is no link between the level of democracy in a country and its income. This is because democracies tend to (not necessarily coincidentally) have other good characteristics.

Cervellati et al. (2004) found that never-colonies benefited from democracy whereas countries that had once been colonies did worse if they were democratic.

Barro (1996) found that democracy was slightly negative for growth once you account for variables like the rule of law, small governments, free markets and human capital (i.e. skills, education and cognitive ability)

That the evidence suggests democracies and non-democracies perform about the same might be surprising given the state of public ignorance. In Sam's words "the public is ignorant about politics and lacks even the basic facts that it would need to make sound judgments about political issues."

Perhaps democratic ignorance and expert narrow-mindedness roughly balance out—or perhaps representative democracies and non-democracies both choose similar sorts of people to rule anyway.

Either way, the evidence seems to suggest that insofar as we can help countries to develop, the key institutions we should be supporting are markets, property rights and the rule of law, and considerably less significance should be accorded to democratisation.